There are certain professions where the accountabilities of a role are outside of your direct control i.e. indirect control over resources. Project and product management both fall into this category. Project management roles in technology involve managing a project that crosses the disciplines of engineering, product, support & IT. Product management works with internal stakeholders in engineering, project, support/sales and external customers in order to build a product. Neither of these lists are extensive (and for good reason, they could be very long).
This means that these roles are largely driven by influence; working with and leading colleagues to accomplish tasks that will benefit the business. Influence overs someone can take different forms depending on the type of the relationship that you have with someone, but it often builds upon: trust, communication & empathy.
Starting out my career in a management role, here are some of the things that have helped me: